Math 221: Calculus 3, Spring 2009

Dr. Brenton LeMesurier
lemesurierb "at" cofc.edu
4 Greenway room 103, phone 953-5917

Last revised Tuesday April 14. Newest additions are highlighted in green.

News and Important Dates Coming Up

Monday April 13

In preparation for Test 3, there is now

a practice test 3,

and class notes up to Section 16.6 on Parametric Surfaces.

Tuesday April 14

There are more corrections to the notes.

Thursday April 16

Test 3, covering Sections 12.7 and 15.7 to 16.6.

Wednesday May 6, 8-11 am

Final Exam

Handouts

• A Practice Test 1.
• A Practice Test 2.
• A Practice Test 3.
• The course note handouts to Section 16.3.
  • Title Page
  • Foreword
  • Organizational Details, like test dates (pages iii and iv.)
  • Homework Exercises revised January 26 (pages v and vi.)
  • Important dates like tests. (page vii.)
  • Corrections to the notes found so far, revised Tuesday April 14. (page viii.)
  • Chapter 12. Vectors and the Geometry of Space.
    • Chapter 12, Section 1. Three-Dimensional Coordinate Systems
    • Chapter 12, Section 2. Vectors
    • Chapter 12, Section 3. The Dot Product (Scalar Product)
    • Chapter 12, Section 4. The Cross Product (Vector Product)
    • Chapter 12, Section 5. Equations of Lines and Planes
    • Chapter 12, Section 6. Cylinders and Quadric Surfaces
    • Postponed: Chapter 12, Section 7. Cylindrical and Spherical Coordinates
  • Chapter 13. Vector Functions
    • Chapter 13, Section 1. Vector Functions and Space Curves
    • Chapter 13, Section 2. Derivatives and Integrals of Vector Functions
    • Chapter 13, Section 3. Arc Length and Curvature
    • Chapter 13, Section 4. Motion in Space: Velocity and Acceleration
  • Chapter 14. Partial Derivatives
    • Chapter 14, Section 1. Functions of Several Variables
    • Chapter 14, Section 2. Limits and Continuity
    • Chapter 14, Section 3. Partial Derivatives
    • Chapter 14, Section 4. Tangent Planes and Linear Approximations
    • Chapter 14, Section 5. The Chain Rule
    • Chapter 14, Section 6. Directional Derivatives and the Gradient Vector
    • Chapter 14, Section 7. Maximum and minimum Values
    • Chapter 14, Section 8. Lagrange Multipliers (Finding Extrema Subject Constraints)
  • Chapter 15. Multiple Integrals
    • Chapter 15, Section 1. Double Integrals over Rectangles
    • Chapter 15, Section 2. Iterated Integrals
    • Chapter 15, Section 3. Double Integrals over General Regions
    • Chapter 15, Section 4. Double Integrals in Polar Coordinates
    • Section 5 is omitted
    • Chapter 15, Section 6. Surface Area
      The material for Test 3 starts here, with further coverage of Section 15.7 which was partially covered on Test 2.
    • Chapter 15, Section 7. Triple Integrals
    • A detour to Chapter 12, Section 7. Cylindrical and Spherical Coordinates
    • Chapter 15, Section 8 Triple Integrals in Cylindrical and Spherical Coordinates
    • Chapter 15, Section 9. Change of Variables in Multiple Integrals
  • Chapter 16. Vector Calculus
    • Chapter 16, Section 1. Vector Fields
    • Chapter 16, Section 2. Line Integrals (and Path Integrals)
    • Chapter 16, Section 3. The Fundamental Theorem for Line (and Path) Integrals
    • Chapter 16, Section 4. Green's Theorem
    • Chapter 16, Section 5. Curl and Divergence
    • Chapter 16, Section 6. Parametric Surfaces and Their Areas
      Test 3 will cover to here, Section 16.6.
      Then the semester will conclude with the following, notes still to come:
    • Chapter 16, Section 7. Surface Integrals
    • Chapter 16, Section 8. Stoke's Theorem
    • Chapter 16, Section 9. The Divergence Theorem